What is ln(9/(5x^5y)) ?

The solution to ln(9/(5x^5y)) is 2ln(3)-ln(5)-5ln(x)-ln(y)

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simplify ln(9/(5x^5y))

simplify

ln (\frac{9}{5 x ^{5} y})

2 ln (3) - ln (5) - 5 ln (x) - ln (y)

Solution steps

ln (\frac{9}{5 x ^{5} y})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{9}{5 x ^{5} y}) = ln (9) - ln (5 x^{5} y)

= ln (9) - ln (5 x^{5} y)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (5 x^{5} y) = ln (5) + ln (x^{5}) + ln (y)

= ln (9) - (ln (x^{5}) + ln (y) + ln (5))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{5}) = 5 ln (x)

= ln (9) - (ln (5) + 5 ln (x) + ln (y))

ln (9) = 2 ln (3)

= 2 ln (3) - (5 ln (x) + ln (y) + ln (5))

- (ln (5) + 5 ln (x) + ln (y)) : - ln (5) - 5 ln (x) - ln (y)

= 2 ln (3) - ln (5) - 5 ln (x) - ln (y)

\frac{ln ( \frac{5}{9} ) + 2 ln ( 13 )}{6 ln ( 13 )}

lo g_{15} (\frac{x}{y})

lo g_{10} (P) - lo g_{10} (Q) - lo g_{10} (R)

ln (\frac{x + 2}{x - 2})

ln (f g)

What is ln(9/(5x^5y)) ?
The solution to ln(9/(5x^5y)) is 2ln(3)-ln(5)-5ln(x)-ln(y)